Put the lid on the container, and ensure complete darkness 24/7.
To monitor the curing (often called cycling the tank) you need to check the levels of ammonia, nitrite, and nitrate. Even if you’ve bought previously cured live rock, you should still follow this process anyway as it is likely there will still be a small cycle. At first, test the water every day for ammonia until the ammonia drops to 0 and stays there for 3 days straight. If the ammonia goes above 2 ppm do a 75-100% waterchange right away to prevent the high ammonia from killing off beneficial life on your live rock, repeat whenever the ammonia goes over 1 ppm (or even better do waterchanges if it goes over 0.5 ppm). Feel free to do as many waterchanges as you want...go ahead and do 50% everyday if you feel so inclined. This will increase the biodiversity on the rocks that survive the cycle.
NOTE- it is a myth that doing waterchanges will slow down the cycle. The reasoning behind that myth is that you are removing nitrifying bacteria in the water column and dumping them down the drain. These are the nitrifying bacteria whose population you are trying to increase as quickly as possible to finish the cycle as quickly as possible. The reason this is a myth is because there is very little nitrifying bacteria in the water column to begin with. The nitrifying bacteria mainly colonize the rocks, sand, and other surfaces. There is a small amount that colonize the water column, but it is not significant enough to slow the cycling process.
After the ammonia drops to 0 you don't need to test for it anymore. You can start testing once or twice a week for nitrite, but you can skip nitrite and just test for nitrate if you want. Nitrite isn't toxic in saltwater aquaria as it is in freshwater aquaria. To clarify:
If testing for nitrite, once nitrite drops to 0 you don't need to test for it anymore either. It may be at 0 when your ammonia gets to 0, or it may take some while yet. Once both the ammonia and the nitrite are at 0 and have been there for a week do a 50-75% waterchange siphoning out as much detritus as you can see including sucking it off the rocks.
If you are not testing for nitrite, wait a week then do a 50-75% waterchange siphoning out as much detritus as you can see including sucking it off the rocks.
Swish the rocks in the tub to remove detritus before doing waterchanges. Using a turkey baster helps. Be sure to leave the rock exposed for as little time as possible. When the ammonia, and nitrite both reach 0 is when most people will put their rock into their aquariums, this is when the curing process is over.
Cooking the Live Rock in a Rubbermaid
If the live rock is already cured, and you would like to continue on to cook the live rock, continue to do 100% waterchanges once a week. Once your nitrite drops to 0, stop testing for it, and test for nitrate. It may take quite some time for nitrate to drop to 0 (possibly several weeks, maybe even a couple months), but when it does you can then stop testing for it, and start testing for phosphate. Be sure to use a high quality test kit (I prefer Salifert for phosphate). Like the nitrate, it may take quite some time for it to drop to 0. Once it does drop to 0, and stays there for a couple weeks test ammonia, nitrite, nitrate, and phosphate. If all are 0, you have successfully cooked your live rock. Give yourself a pat on the back for your patience, it will pay off!
The only downfall that I have noticed of cooking liverock is the die off of a good amount of coralline algae. I think the benefits of cooking the live rock hugely outweigh this though. The coralline actually comes back very quickly under healthy conditions.